Except the shiny new UK Nook store doesn't have an option to download a book you have bought, only way I can get a copy onto my PC is to download the book to the android app, copy the book from the app folder to a folder that is visible to the PC when I plug in the phone, copy from the phone to the PC.

I've got it one step quicker than that. After downloading in the Android app, navigate to the Nook content folder in a file manager and send the book to Dropbox or Google Drive. At least the download to the PC part's automatic!